Data-driven discovery for vibration energy harvesters with white Gaussian noise

Abstract Multi-stable vibration energy harvesters (VEHs) are low-energy consumption devices and self-powered core devices for wireless sensor networks. However, it is difficult to model their stochastic differential equations (SDEs) under noise excitation. Traditional sparse regression relies on artificial preset basis functions, which is not suitable for complex nonlinear systems. Aiming at this core problem, this paper introduces an evolutionary symbolic sparse regression (ESSR) method to solve its stochastic dynamic modeling problem. The method realizes the adaptive evolution of the basis function by genetic programming, synchronously models multiple response variables with multi-tree coding, and outputs a high-precision explicit analytical model by iteratively screening the fitting drift term and diffusion term. This method provides reliable support for multi-steady-state VEHs modeling, can promote its application in the optimization of self-powered systems, and also provides technical reference for multi-domain nonlinear system identification.